A posteriori error estimates and adaptive stopping criteria for a compositional two-phase flow with nonlinear complementarity constraints

Abstract : In this work, we develop an a-posteriori-steered algorithm for a compositional two-phase flow with exchange of components between the phases in porous media. As a model problem, we choose the two-phase liquid-gas flow with appearance and disappearance of the gas phase formulated as a system of nonlinear evolutive partial differential equations with nonlinear complementarity constraints. The discretization of our model is based on the backward Euler scheme in time and the finite volume scheme in space. The resulting nonlinear system is solved via an inexact semismooth Newton method. The key ingredient for the a posteriori analysis are the discretization, linearization, and algebraic flux reconstructions allowing to devise estimators for each error component. These enable to formulate criteria for stopping the iterative algebraic solver and the iterative linearization solver whenever the corresponding error components do not affect significantly the overall error. Numerical experiments are performed using the Newton-min algorithm as well as the Newton-Fischer-Burmeister algorithm in combination with the GMRES iterative linear solver to show the efficiency of the proposed adaptive method.
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Ibtihel Ben Gharbia, Jad Dabaghi, Vincent Martin, Martin Vohralík. A posteriori error estimates and adaptive stopping criteria for a compositional two-phase flow with nonlinear complementarity constraints. Computational Geosciences, Springer Verlag, 2019, ⟨10.1007/s10596-019-09909-5⟩. ⟨hal-01919067v3⟩

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